ACAT05 May 22 - 27, 2005 DESY, Zeuthen, Germany The use of Clustering Techniques for the Classification of High Energy Physics Data Mostafa MJAHED Ecole.

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Presentation on theme: "ACAT05 May 22 - 27, 2005 DESY, Zeuthen, Germany The use of Clustering Techniques for the Classification of High Energy Physics Data Mostafa MJAHED Ecole."— Presentation transcript:

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ACAT05 May , 2005 DESY, Zeuthen, Germany The use of Clustering Techniques for the Classification of High Energy Physics Data Mostafa MJAHED Ecole Royale de lAir, Mathematics and Systems Dept. Marrakech, Morocco

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Production of jets in e + e - Production of jets in e + e - Methodology Methodology The use of Clustering Techniques for the Classification of physics processes in e + e - The use of Clustering Techniques for the Classification of physics processes in e + e - Conclusion Conclusion The use of Clustering Techniques for the Classification of High Energy Physics Data M. Mjahed ACAT 05, DESY, Zeuthen, 25 May

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Jets analysis in e + e - These analyses are subjected to the identification of the different processes, with dominant jets topologies with a very high efficiency Analysis of W bosons pairs and research of new particles as the Higgs boson. Prediction of limits concerning the mass of the Higgs boson Measure of the masse of W Measure of the Triple Gauge Coupling (TGC); coupling between 3 bosons Need to use Pattern Recognition methods

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K-Means Clustering Technique Given K, the K-means algorithm is implemented in 4 steps: Partition events into K non empty subsets Compute seed points as the centroids (mean point) of the cluster Assign each event to the cluster with the nearest seed point Go back to step 2, stop when no more new assignment Parameters: Choice of distances Supervised or unsupervised Learning M. Mjahed ACAT 05, DESY, Zeuthen, 25 May

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Clustering by a Peano Scanning Technique Example of an analytical Peano square-filling curve Decomposition of data into p-dimensional unit hyper-cube I p = [0, 1] [0, 1] … [0, 1] Construction of a Space Filling Curve (SFC) F p (t): I 1 I p Compute the position of X (data) on the SFC, i.e., t = (x) Find the set K of nearest neighbours of t in the transformed learning set T Classify the test sample to the nearest class in set K

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Efficiency and Purity of a Pattern Recognition Method Efficiency of classification for events of class C i Purity of classification for events of class C i Validation Test events M. Mjahed ACAT 05, DESY, Zeuthen, 25 May

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Discriminating Power of variables Test Function F j, j=1, …, 17. B j,W j : Between and Within-classes Variance Matrix for variable j. n total number of events (signal+ background), k number of classes (2) The discriminating power of each variable V j is proportional to the values of F j (j=1, …, 17).

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K-Means Clustering Classification C C HZ C Back For K=2, the K-means algorithm is implemented in 4 steps: Partition events into 2 non empty subsets Compute seed points as the centroids (mean point) of the cluster Assign each event to the cluster with the nearest seed point Go back to step 2, stop when no more new assignment Classification of test events

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Conclusion (continued) Methods Importance of Pattern Recognition Methods The improvement of an any identification is subjected to the multiplication of multidimensional effect offered by PR methods and the discriminating power of the proposed variable. Clustering techniques: comparative to other statistical methods : Discriminant Analysis, Decision trees,... Clustering techniques: less effective than neural networks and non linear discriminant analysis methods The hierarchical clustering method is more efficient than the other clustering techniques: its performances are in average 1 to 3 % higher than those obtained with the two other methods. Other cut's values D HZ/Back * give other efficiencies and purities: We can reach values of purity permitting to identify the HZ events more efficiently